bugs - NotebookEvaluate breaks notebook's context

Bug introduced in 10.4.1 or earlier and persists through 11.3

A support case with the identification [CASE:3813108] was created

[...] I have forwarded an incident report to our developers with the information you provided [...]

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Here is an example of a notebook with local context:

nb = CreateDocument[{

  ExpressionCell[Defer @ CurrentValue[EvaluationNotebook[], CellContext], "Input"],
  ExpressionCell[Defer @ $Context, "Input"]
 },
 CellContext -> Notebook
]

Let's NotebookEvaluate it twice:

NotebookEvaluate[nb, InsertResults -> True]

"Notebook$$35$971589`"

NotebookEvaluate[nb, InsertResults -> True]

"Global`"

We can see that the first evaluation was done with respect to the local context but left the notebook broken. It now works with Global` context despite CellContext->Notebook.

According to NotebookEvaluate / Possible Issues one should expect "Notebook$$35$971589"` each time. Ok, one could arguee here but everyone will probably agree that the result should at least be consistent each time.

Is this a bug or have I missed something?

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Related:

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[...] A possible fix to this had been suggested in the previous email. [...]

Which is to use CellContext->Notebook as an explicit option for each cell.